We propose a novel method for constructing illusory foreground and background shapes from convex corners. We first introduce a new class of visual cues called corner bases, which expands zero-dimensional corner points to two-dimensional microstructures. These corner bases are then fused together by the functionalized elastica energy imposed upon an admissible phase field. The optimal phase field segments the visual field into disjoint connected components, which are further fused via a simple connectivity principle to construct both foreground illusory shapes and background occluded shapes. Robust and efficient numerical schemes are developed, and several generic examples are presented. Cognitive implications are highlighted.

We present a novel coupled filter pair for denoising, segmentation, and inpainting, based on the well known Mumford-Shah image model. Our self-contained digital extension to a general graph domain makes it possible to cheaply and universally benefit from this conventionally expensive yet very powerful image model.

Motivated by the classical TV (total variation) restoration model, we propose a new nonlinear filter-the digital TV filter for denoising and enhancing digital images, or more generally, data living on graphs. The digital TV filter is a data dependent lowpass filter, capable of denoising data without blurring jumps or edges. In iterations, it solves a global total variational (or L(1)) optimization problem, which differs from most statistical filters. Applications are given in the denoising of one dimensional (1-D) signals, two-dimensional (2-D) data with irregular structures, gray scale and color images, and nonflat image features such as chromaticity.